14 - finite element method

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14 - finite element method
14 - finite element method - volume growth -
theory
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finite element method
from continuous problem
temporal discretization
implicit euler backward
spatial discretization
finite element method
staggered solution
newton raphson iteration
linearization
gateaux derivative
to linearized discrete initial boundary value
problem
3
finite element method
integration point based
discrete residual
compare integration point based density growth!
discrete residual
difference only in stress calculation _at_ int point!
discrete residual
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finite element method
integration point based
discrete residual
check in matlab!
residual of mechanical equilibrium/balance of
momentum
discrete residual
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finite element method
integration point based
linearization / newton raphson scheme
incremental residual
system of equations
incremental iterative update
linearization
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finite element method
integration point based
stiffness matrix / iteration matrix
compare integration point based density growth!
linearization of residual wrt nodal dofs
difference only in stress calculation _at_ int point!
linearization
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finite element method
integration point based
stiffness matrix / iteration matrix
check in matlab!
linearization of residual wrt nodal dofs
linearization
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finite element method
integration point based
constitutive equations - given calculate
with
and
with
evolution of internal variable
with
and
constitutive equations
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finite element method
integration point based
constitutive equations - given calculate
check in matlab!
stress calculation _at_ integration point level
constitutive equations
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finite element method
integration point based
constitutive equations - given calculate
temporal discretization - euler implizit
local newton iteration
with
constitutive equations
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finite element method
integration point based
residual
linearization of residual
with
constitutive equations
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finite element method
stress driven volume growth
13
finite element method
integration point based
discrete volume update
check in matlab!
residual of biological equilibrium / volume
growth
constitutive equations
14
finite element method
integration point based
constitutive equations - given calculate
with
depends on time discretization
constitutive equations
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finite element method
integration point based
tangent operator / constitutive moduli
check in matlab!
linearization of stress wrt deformation gradient
constitutive equations
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finite element method
integration point based
loop over all time steps
global newton iteration
loop over all elements
loop over all quadrature points
local newton iteration to determine
determine element residual partial derivative
determine global residual and iterational matrix
determine
determine state of biological equilibrium
staggered solution